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Changes between Version 9 and Version 10 of OfficialTolArchiveNetworkQltvRespModel


Ignore:
Timestamp:
Dec 21, 2010, 11:53:10 AM (15 years ago)
Author:
Víctor de Buen Remiro
Comment:

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  • OfficialTolArchiveNetworkQltvRespModel

    v9 v10  
    8989In this case we have that scalar distribution is the standard normal one.
    9090
    91   [[LatexEquation( F\left(z\right) = F_{0,1}\left(z\right) )]] [[BR]] [[BR]]
     91  [[LatexEquation( F\left(z\right) = \Phi\left(z\right) )]] [[BR]] [[BR]]
    9292
    93   [[LatexEquation( f\left(z\right) = f_{0,1}\left(z\right) )]] [[BR]] [[BR]]
     93  [[LatexEquation( f\left(z\right) = \phi\left(z\right) )]] [[BR]] [[BR]]
    9494
    95   [[LatexEquation( f'\left(z\right) = -z f_{0,1}\left(z\right) )]] [[BR]] [[BR]]
     95  [[LatexEquation( f'\left(z\right) = -z \phi\left(z\right) )]] [[BR]] [[BR]]
    9696
    97   [[LatexEquation( L\left(\beta\right)=\underset{i}{\sum}w_{i}\left(y_{i}\ln\left(F_{0,1}\left(x_{i}\beta\right)\right)+\left(1-y_{i}\right)\ln\left(1-F_{0,1}\left(x_{i}\beta\right)\right)\right) )]]
     97  [[LatexEquation( L\left(\beta\right)=\underset{i}{\sum}w_{i}\left(y_{i}\ln\left(\Phi\left(x_{i}\beta\right)\right)+\left(1-y_{i}\right)\ln\left(\Phi\left(-x_{i}\beta\right)\right)\right) )]]
    9898
    99   [[LatexEquation( \frac{\partial L\left(\beta\right)}{\partial\beta_{j}}=\underset{i}{\sum}w_{i}\left(y_{i}\frac{f_{0,1}\left(x_{i}\beta\right)}{F_{0,1}\left(x_{i}\beta\right)}-\left(1-y_{i}\right)\frac{f_{0,1}\left(x_{i}\beta\right)}{1-F_{0,1}\left(x_{i}\beta\right)}\right)x_{ij} )]]
     99  [[LatexEquation( \frac{\partial L\left(\beta\right)}{\partial\beta_{j}}=\underset{i}{\sum}w_{i}\left(y_{i}\frac{\phi\left(x_{i}\beta\right)}{\Phi\left(x_{i}\beta\right)}-\left(1-y_{i}\right)\frac{\phi\left(x_{i}\beta\right)}{\Phi\left(-x_{i}\beta\right)}\right)x_{ij} )]]
    100100
    101   [[LatexEquation( \frac{\partial L\left(\beta\right)}{\partial\beta_{i}\partial_{j}}=-\underset{k}{\sum}w_{k}f_{0,1}\left(x_{k}\beta\right)\left(y_{k}\frac{zF_{0,1}\left(x_{k}\beta\right)+f_{0,1}\left(x_{k}\beta\right)}{F_{0,1}^{2}\left(x_{k}\beta\right)}+\left(1-y_{k}\right)\frac{-z\left(1-F_{0,1}\left(x_{k}\beta\right)\right)+f_{0,1}\left(x_{k}\beta\right)}{\left(1-F_{0,1}\left(x_{k}\beta\right)\right)^{2}}\right)x_{ik}x_{jk} )]]
     101  [[LatexEquation( \frac{\partial L\left(\beta\right)}{\partial\beta_{i}\partial_{j}}=-\underset{k}{\sum}w_{k}\phi\left(x_{k}\beta\right)\left(y_{k}\frac{z\Phi\left(x_{k}\beta\right)+\phi\left(x_{k}\beta\right)}{\Phi^{2}\left(x_{k}\beta\right)}+\left(1-y_{k}\right)\frac{-z \Phi\left(-x_{k}\beta\right)+\phi\left(x_{k}\beta\right)}{\Phi\left(-x_{k}\beta\right)^{2}}\right)x_{ik}x_{jk} )]]